A Comprehensive study of arithmetic circuits and elliptic curves for efficient and scalable zero-knowledge proof systems

In recent years, zero-knowledge proofs have come to play a crucial role in distributed systems where there is no trust between the parties involved. Most popular proof systems are for the NP-complete language of arithmetic circuit satisfiability. Although there have been tremendous efforts in unders...

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Detalles Bibliográficos
Autor: Bellés Muñoz, Marta
Tipo de recurso: tesis doctoral
Estado:Versión publicada
Fecha de publicación:2023
País:España
Institución:CBUC, CESCA
Repositorio:TDR. Tesis Doctorales en Red
OAI Identifier:oai:www.tdx.cat:10803/689318
Acceso en línea:http://hdl.handle.net/10803/689318
Access Level:acceso abierto
Palabra clave:Blockchain
Zero-knowledge proof
Arithmetic circuit
Elliptic curve
Cadena de blocs
Prova de coneixement zero
Circuit aritmètic
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Descripción
Sumario:In recent years, zero-knowledge proofs have come to play a crucial role in distributed systems where there is no trust between the parties involved. Most popular proof systems are for the NP-complete language of arithmetic circuit satisfiability. Although there have been tremendous efforts in understanding, developing, and improving zero-knowledge proof systems, not much work has been done towards the study of arithmetic circuits. In this thesis, we contribute to this matter in three different aspects. First, we present circom, a programming language for writing arithmetic circuits that abstracts the complexity of the proof system. Second, we provide a deterministic algorithm for generating twisted Edwards elliptic curves that can be used to prove elliptic-curve cryptography statements in zero knowledge efficiently. Finally, we explore recursive composition of pairing-based proof systems with native circuit arithmetic, delving into the study of cycles of pairing-friendly elliptic curves of prime order.